Abstract
In this article, we study the double chain deoxyribonucleic acid (DNA) system, the work will be carried out via appropriate transformations. Distinct types of soliton solutions, namely, lump, lump one stripe, lump two stripe, lump periodic and rogue wave solutions will be studied for different polynomial functions. By setting the function as the general quadratic polynomial function, a type of lump solution which contains various parameters will be obtained. We also show an interaction solution with lump, periodic and kink wave respectively. This article also, leads to construct Ma-breather (MB), Kuznetsov-Ma breather (KMB) and its relating rogue wave solutions. Some of the obtained solutions will be graphically exemplified.
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